Creating a custom menu

From the WP Admin menu go to Appearance > Menus and create a menu. Name it whatever you want. From the menus sidebar add whatever pages, custom links or categories you like to the menu you just created. Then, save the menu and add it to one of the available menu locations.

Creating a Blog category

To create a blog section you don’t need any page templates or any similar stuff.
From the WP Admin menu go to Posts > Categories and create a new category. It can have any name you like. Add to it all posts that you want to be shown in the Blog section. Then, from Appearance > Menus, add the category you just created to the header menu for example.